Cryptology ePrint Archive: Report 2009/340

Efficient Indifferentiable Hashing into Ordinary Elliptic Curves

Eric Brier and Jean-Sebastien Coron and Thomas Icart and David Madore and Hugues Randriam and Mehdi Tibouchi

Abstract: We provide the first construction of a hash function into ordinary elliptic curves that is indifferentiable from a random oracle, based on Icart's deterministic encoding from Crypto 2009. While almost as efficient as Icart's encoding, this hash function can be plugged into any cryptosystem that requires hashing into elliptic curves, while not compromising proofs of security in the random oracle model.

We also describe a more general (but less efficient) construction that
works for a large class of encodings into elliptic curves, for example the Shallue-Woestijne-Ulas (SWU) algorithm. Finally we describe the first deterministic encoding algorithm into elliptic curves in characteristic 3.